The course is a standard introduction to Calculus: differential and integral calculus in one variable, some differential equations, differential calculus in two variables. The various topics will be presented mainly via examples and intuitive justifications; in some cases formal proofs will be given. Exercise sessions are very important for the course.
The course aims to provide the essential elements of differential and integral calculus for functions of one variable and those of differential calculus for functions of two variables; it also provides an introduction to ordinary differential equations.
The aim is to provide some fundamental tools of Mathematical Aalysis, to improve the students' attitude toward rigorous reasonig and and to teach students how to solve some problems using the notions studied in the course.
At the end of the course the student must know the fundamental results of the differential calculus in one and two variables and of the integral calculus in one variable. Moreover, the student must know how to apply such notions to solve the exercises, and must be able to apply such notions in other courses that use them.
The standard curriculum of the Italian scuole medie superiori
Traditional: theory lessons, exercises sessions, support by tutors; exercises for independent training are given to students.
Differential calculus in one variable (limits, continuity, derivatives, Taylor formula, study of functions). Integral calculus in one variable (primitives, definite integrals and areas, improper integrals, study of integral functions). Differential equations (separation of variables, linear equations of first order, linear equations with constant coefficients). Differential calculus in two variables (limits, continuity, partial derivatives, level curves, tangent lines and planes, max, min and hessian matrix).
F.Parodi, T.Zolezzi - Appunti di Analisi Matematica - ECIG Genova
M.Baronti. F.De Mari, R.Van der Putten, I.Venturi - Calculus Problems - Springer Italia 2016.
Ricevimento: On appointment; take directly an appointment with the professor or write to perelli@dima.unige.it
ALBERTO PERELLI (President)
ETTORE GIOVANNI CARLETTI
CLAUDIO NICOLINI (President Substitute)
https://corsi.unige.it/8713/p/studenti-orario
Two intermediate written exams (end of first and second semester), final written and oral examination. If students pass both intermediate written exams, the arithmetic mean of the results can be taken as result for the written exam in the summer sessions (June - July - September). If both such intermediate written exams are passed with success, their arithmetic mean can be used as the final mark of the course.
Evaluation of the output from written and oral exams; the goal of the course is reached if the student is able to solve exercises of the same level as those proposed during the exercises hours of the course, and if the student knows the fundamental contents of the course.
Students are recommended to follow all lectures, exercises sessions and tutors hours.
